Question Number 115725 by Bird last updated on 28/Sep/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{lnx}}{\left({x}^{\mathrm{2}\:} +{x}+\mathrm{2}\right)^{\mathrm{2}} }{dx} \\ $$ Answered by mathmax by abdo last updated on 28/Sep/20…
Question Number 50186 by rahul 19 last updated on 14/Dec/18 $${Let}\:{f}\left({x}\right)=\:\int_{\mathrm{2}} ^{\:{x}} \:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{6}} }. \\ $$$${Prove}\:{that}\:\::\:\frac{\mathrm{1}}{\mathrm{730}}<{f}\left(\mathrm{3}\right)<\frac{\mathrm{1}}{\mathrm{65}}. \\ $$ Answered by mr W last updated on…
Question Number 50161 by cesar.marval.larez@gmail.com last updated on 14/Dec/18 $${Find}\:{the}\:{function}\:{whose}\:{first}\: \\ $$$${derivative}\:{is}\:\mathrm{8}−\frac{\mathrm{5}}{\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} }}\:{the}\:{initial}\: \\ $$$${conditions}\:{f}\left(\mathrm{8}\right)=−\mathrm{20} \\ $$ Answered by afachri last updated on 14/Dec/18 $${F}\left({x}\right)\:\:=\:\:\int\:{f}'\left({x}\right)\:\:{dx}…
Question Number 50158 by cesar.marval.larez@gmail.com last updated on 14/Dec/18 Commented by cesar.marval.larez@gmail.com last updated on 14/Dec/18 $${i}\:{am}\:{practicing}\:{very}\:{hard} \\ $$ Answered by afachri last updated on…
Question Number 115689 by Algoritm last updated on 27/Sep/20 Answered by mathmax by abdo last updated on 27/Sep/20 $$\mathrm{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{x}+\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\right)}{\mathrm{x}}\mathrm{dx}\:\:\mathrm{changement}\:\mathrm{x}\:=\mathrm{sint}\:\mathrm{give} \\ $$$$\mathrm{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 115664 by bemath last updated on 27/Sep/20 $${If}\:\underset{{x}\rightarrow{p}} {\mathrm{lim}}\:\frac{{p}^{{x}} −{x}^{{p}} }{{x}^{{x}} −{p}^{{p}} }\:=\:\mathrm{1}\:{then}\:{p}\:=\:? \\ $$ Answered by Olaf last updated on 27/Sep/20 $${x}\:=\:{p}+{u}…
Question Number 115656 by bobhans last updated on 27/Sep/20 $$\int\:\sqrt{\frac{{x}−{a}}{{b}−{x}}}\:{dx}\:=\:? \\ $$$${where}\:{a}\:<{x}\:<\:{b} \\ $$ Commented by bemath last updated on 27/Sep/20 $${I}=\:\int\:\sqrt{\frac{{x}−{a}}{−{x}+{b}}}\:{dx}\: \\ $$$${I}\:=\:−\sqrt{\left({x}−{a}\right)\left({b}−{x}\right)}\:−\left({a}+{b}\right)\mathrm{sin}^{−\mathrm{1}} \left(\sqrt{\frac{{b}−{x}}{{a}+{b}}}\right)+{C}…
Question Number 115661 by bemath last updated on 27/Sep/20 $$\left(\mathrm{1}\right)\:\int\:\mathrm{sin}\:\left(\sqrt{{x}}\right)\:{dx} \\ $$$$\left(\mathrm{2}\right)\:\int\:\mathrm{cos}\:\left(\sqrt{{x}}\:\right)\:{dx}\: \\ $$$$\left(\mathrm{3}\right)\:\int\:\mathrm{tan}\:\left(\sqrt{{x}}\:\right)\:{dx}\: \\ $$ Answered by Dwaipayan Shikari last updated on 27/Sep/20 $$\int\mathrm{sin}\left(\sqrt{\mathrm{x}}\right)\mathrm{dx}\:\:\:\:\:\:\:\:\:\mathrm{x}=\mathrm{t}^{\mathrm{2}}…
Question Number 181152 by amin96 last updated on 22/Nov/22 $$\boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{integral}} \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{{x}}\right)\boldsymbol{{ln}}\left(\mathrm{1}−\boldsymbol{{x}}\right)}{\mathrm{1}+\boldsymbol{{x}}}\boldsymbol{{dx}}=??? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 115594 by MJS_new last updated on 26/Sep/20 $$\mathrm{old}\:\mathrm{question},\:\mathrm{I}\:\mathrm{couldn}'\mathrm{t}\:\mathrm{find}\:\mathrm{it}: \\ $$$$\int\sqrt{{x}−\sqrt{{x}}}{dx}=? \\ $$ Answered by MJS_new last updated on 26/Sep/20 $$\int\sqrt{{x}−\sqrt{{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{{x}}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{{x}}{dt}\right] \\…